A conventional receiver structure in a wideband system covering a range of DC to several tens of Gigahertz is composed of a search system for signal detection and multiple narrowband receivers for signal processing as shown in FIG. 1. Traditional search systems rely on the frequency sweeping approach where a receiver sweeps through frequencies within a range to detect signals. To provide wideband spectral coverage, the search system either uses a channelized approach, where the search receiver is actually made of multiple receivers, each covering a small frequency band, or use one receiver that sweeps through the entire band over a long period. FIG. 1 shows the prior art channelized approach.
Compressive sensing theory (CS) was introduced by Candes (E. Candes and T. Tao, “Near optimal signal recovery from random projection: universal encoding strategies?” IEEE Trans. on Information Theory, 52:5406-5425, 2006.) and Donoho (D. L. Donoho, “Compressed sensing”, IEEE Trans. on Information Theory, 52:1289-1306, 2006). Compressive sensing has been adopted in many applications including signal detection and reconstruction, to save sampling resources. The advantage of applying compressive sensing techniques to signal detection is that compressive sensing measurements incorporate a hologram of the entire spectrum in each measurement. As long as sparsity conditions are met, signals can be detected with far fewer measurements without sweeping through the spectrum.
For the compressive sensing theory to be applicable, the signal should be sparse (or compressible) in a certain domain and the sampling basis should be incoherent with the sparse domain. When the signal is discrete, random matrices whose entries are made of random numbers identically and independently drawn from a normal distribution or a symmetric Bernoulli distribution are often proposed as the sampling matrices. With a high probability, such sampling matrices are incoherent with most basis of the sparse domain. Hence, compressive sampling and reconstruction techniques can be widely applied to many different types of signals. However, this pure random sampling basis is not applicable for sampling analog signals because they are discrete in nature. Modified versions of the random basis have been proposed to sample analog signals compressively. See, for example:
Joel A. Tropp, Jason N. Laska, Marco F. Duarte, Justin K. Romberg, and Richard G. Baraniuk, “Beyond nyquist: efficient sampling of sparse bandlimited signals”, IEEE Trans. on Information Theory, 56:520-544, 2010. The input signal is modulated by a pseudorandom sequence and then the modulated signal is integrated and sampled at a regular rate lower than the Nyquist rate, as shown in FIG. 2a. 
Moshe Mishali and Yonina C. Eldar, “From theory to practice: Sub-nyquist sampling of sparse wideband analog signals”, IEEE Journal of Selected Topics in Signal Processing, 4:375 391, 2010. This approach takes a similar approach as Tropp in the front end and also modulates the signal by a pseudorandom sequence. The modulated signal passes through a lowpass filter and samples are directly taken from the filtered signal without integrating it, as shown in FIG. 2c 
Xiangming Kong, Peter Petre, and Roy Matic, “An analog-to-information converter for wideband signals using a time encoding machine”, IEEE 14th DSP Workshop, pp. 414-419, 2011. This approach takes a different path. It first converts the amplitude information of the signal to time information through a time encoder and measures the time information asynchronously. In converting the signal, the feedback gain in the time encoder is set to be a random sequence to randomize the sampling process. This procedure is illustrated in FIG. 2b. 
A common characteristic of these approaches is that the frequency information of the input signal x(t) over the entire sampling period is mixed and measured together in one data bunch. One drawback of this approach is that it can only handle frequency sparse signals, such as input made up of several narrowband signals. But in reality, if we observe the spectrum over a long period, we will find it is seldom sparse as required in these prior techniques. Instead, it is “instantly sparse”, i.e. many signals only last a short period and hence only a small portion of the spectrum is occupied in any instant. Strictly speaking, these signal environments are time-frequency sparse. The prior techniques discussed above cannot work effectively in such environments. More importantly, in the prior techniques discussed above, when there are unwanted interfering signals, information from these signals cannot be removed at the sampling stage. Instead, these techniques rely on the reconstruction algorithms to locate the interfering signals, reconstruct them and possibly throw them away in the future. There are two problems associated with this approach. Firstly, due to the existence of the interfering signals (or interference signals), the sparsity of the spectrum reduced. Then to obtain the reconstruction, a large number of measurements need to be collected over a long time period. The overall spectrum over this long time period may not be sparse enough to obtain a good reconstruction. Even if the spectrum remains sparse, the reconstructed interference signals are only accurate to the extent the frequency grids of the representation basis allow. In reality, the frequency band of a signal is usually continuous. Hence, the interference signals cannot be reconstructed accurately and impair the reconstruction quality of other signals as well. The approach in the Mishali paper deals with continuous band directly and is less affected by this problem. However, since the number of measurement channels it requires has to be at least twice as large as the number of signals present, its resource usage efficiency is much lower than the dynamic resource allocation approach disclosed herein.
In this disclosure, a new scheme for sampling time-frequency sparse signal is presented. A compressive sensing technique is applied to the sampling process to reach simultaneous coverage of the entire supported band. Compared to existing compressive sensing approaches, an important feature of this scheme is the addition of an interference removal procedure in the sampling process. By the use of an interference removal procedure in the sampling process, a smaller number of samples are needed to process the input signal than the prior techniques discussed above and has a much lower sparsity requirement on the spectrum. At the same time, resources are allocated to reconstruct a signal preferably only after it is detected and a central frequency is determined. This dynamic resource allocation procedure improves the resource usage efficiency.
A compressive sensing procedure reduces the usage of sampling resource at the price of a complex reconstruction algorithm. Typically the reconstruction algorithm contains iterative optimization procedures. Therefore, another major drawback existing in the current compressive signal detection and reconstruction algorithms is that they cannot do real-time processing due to the need for such iterative optimization procedures. However, in many applications, such as electronic warfare, ability to do real-time processing and to adapt to a highly dynamic environment is critical to the success of an operation. The new scheme presented in this disclosure avoids the complex computation required by existing compressive sensing reconstruction algorithms and process the signal in real time so that it can quickly adapt to highly dynamic environments.